1. Optical disk-based correlators
Optical disk correlators using 2-dimensional (planar) holograms are well-known in the art. Askar Kutanov et al., "Holographic-Disk-Based Optical Neural Network, Optics Letters, Vol. 17, No. 13 (Jul. 1, 1992), discloses an optical disk-based correlator in which the Fourier transforms of the input image and the hologram are multiplied on disk. Demetri Psaltis et al., "Optical Memory Disks in Optical Information Processing," Applied Optics, Vol. 29, No. 14, 10 May 1990, pages 2038-2057 discusses the VanderLugt correlator, the photorefractive correlator and the rotating mirror correlator, which are three basic types of optical disk correlators employing two-dimensional digitally recorded images or holograms in a commercial digital reflective optical disk (such as a standard CD disk). Such devices store only one hologram in each location or recording spot on the disk.
The VanderLugt correlator is illustrated in FIG. 1a and includes an optical disk 10 on which is recorded a digital computer-generated Fourier transform hologram 12. The product of the Fourier transform of an input image 14 obtained through a spherical lens 16 and the Fourier transform hologram 12 is formed at the disk 10 and an inverse transform of this product (through the spherical lens 16) yields a 2-dimensional correlation function in an output plane 18. The VandeLugt correlator of FIG. 1a exemplifies the theorem that the correlation of two functions in the image plane is the product of their Fourier transforms in the spatial frequency domain.
In the photorefractive optical disk-based correlator of FIG. 1b, the disk 10 stores a series of digital template images 20 (not holograms) in separate recording spots rather than their Fourier transforms. Before a template image 20 is read off of the disk 10, the Fourier transform of the input image 14 (obtained through the spherical lens 16) is combined with a reference beam 22 to form a temporary hologram in an optical medium 24. Then, the image 20 is illuminated by a disk illumination beam 26 while the input beam 14 is blocked. The Fourier transform of the on-disk image 20 (obtained through the lens 16) combines with the temporary hologram in the optical medium 24. The Fourier transform of this product (obtained through a second spherical lens 28) yields the correlation image in the plane 18. If the medium 24 is a thin holographic plate, then the correlation function at the correlation plane 18 is a true 2-dimensional correlation function of the image of the input beam 14 and the template image 20. On the other hand, if the optical medium is a solid photorefractive crystal, then the image at the correlation plane is only a 1-dimensional slice of the correlation function. In order to generate the full 2-dimensional correlation function, the disk 10 is rotated to spatially shift the image so that a line detector in the correlation plane 18 detects successive 1-dimensional slices of the correlation function.
While the correlators of FIGS. 1a and 1b perform correlations in the frequency domain, the rotating mirror correlator of FIG. 1c performs correlation in the image plane. Specifically, in FIG. 1c the image (not a hologram) digitally recorded on the disk 10 is that of the template image, not its Fourier transform, and the input image 32 combines with the template image 30 in the disk 10 to form their inner product image at a single pixel detector 34. A two-dimensional array of such inner products forming the full 2-dimensional correlation function is obtained by rotating the disk 30 through the along-track width of the image 30 while the input image scans the radial height of the image 30 by means of a rotating mirror 36. Simultaneously, the output of the single pixel detector is read out in synchronism with the disk and mirror rotation. In order to increase read-out speed, the rotating mirror may be replaced by a Bragg cell or acousto-optic device (not shown) which shifts the input image in synchronism with an RF chirp signal controlling the acousto-optic device.
2. Inner products from volume (3-dimensional) holograms
Solid Lithium Niobate crystals have been used to generate and store volume Fourier transform holograms of template images. By reading these holograms out with an input beam of an unknown Fourier transform image, the inner product and a one-dimensional slice of the correlation function of the input image with each template image are detected. For example, referring to FIG. 2a, a letter "A" input image 39 from an input plane 40, Fourier transformed by a spherical lens 42, and a reference beam (which has been Fourier transformed into a plane wave by a spherical lens 43) from a reference plane 44 interfere together in a solid Lithium Niobate crystal 46. The resulting interference pattern creates an electro-optical pattern 48 (shown in FIG. 3a) in the crystal 46 which remains after the interfering waves are removed.
Referring to FIG. 3a, an unknown image 50 (corresponding roughly to the letter "B") in the input plane 40 is Fourier transformed by the spherical lens 42 and diffracted by the pattern 48 in the crystal 46 to form an output beam 52. The output beam 52 is Fourier transformed by a second spherical lens 54 at an output plane 56. The output plane 56 is depicted in FIG. 3b along with the amplitude of the received light 60. The received light 60 is sensed along a column 62 in the Y direction whose X intercept is related to the X component of the location of the reference beam in the reference plane 44. The received light 60, or detected pattern, sensed along the column 62 is a sequence of inner products between the input image and shifted versions of the template image (shifted in the Y direction), which is a 1-dimensional slice of the 2-dimensional correlation function of the reference and input images. Thus, the received light 60, or detected pattern, may be referred to as a one-dimensional slice of a two-dimensional correlation function. The peak 64 of the one-dimensional correlation slice 60 is the best matched inner product.
The principal advantage of 3-dimensional holograms in the solid crystal 46 is that many images can be recorded in one spot using angular multiplexing. Referring to FIGS. 2a, 2b and 2c, three different template image holograms (corresponding to the letters "A", "B" and "C") are recorded in the solid crystal using reference beams originating at locations with three different X intercepts in the reference plane 44. These three different locations are Fourier transformed by the spherical lens 43 to three different plane wave angles, so that the three reference beams enter the crystal at three different angles. During diffraction of the input beam by the holographic pattern 48 in FIG. 3a, the diffracted beam consists of three plane waves at three different angles. The spherical lens 54 Fourier transforms these angles into three different X-axis intercepts in the output plane 56, so that three different one-dimensional correlation slices 60, 66, 68 with the three respective template images are viewed along three different columns 62, 70, 72 along the X-axis of the output plane 56, each column 62, 70, 72 corresponding to the angle of a corresponding reference beam in the reference plane 44 of FIGS. 2a, 2b, 2c. Since the input image 50 most closely resembles the template image "B", the middle correlation slice 66 has the highest peak in FIG. 3b.
While the foregoing example discusses the recording of only three template images in the same spot in the crystal 46, it is possible to separately record thousands of different images in the same spot using angular multiplexing. While this feature assures extremely high inner product computation rates, a disadvantage of the volume hologram technique of FIGS. 3a and 3b is that a correlation function is available only in one dimension (along the Y axis in the output plane 56), so that the technique is practical only for obtaining inner products and one-dimensional correlation slices between images. In addition, the individual diffraction efficiency decreases by the inverse square of the number of angularly multiplexed holograms in a single spot. Therefore, the light efficiency decreases quickly with the number of holograms.
A disadvantage of the optical disk based correlators of FIGS. 1a, 1b and 1c is that their correlation rates and storage capacities are limited, and there has seemed to be no simple way to dramatically increase the correlation rate and storage capacity of a disk-based correlator.